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Compartmental models with transfer delays: a semi-Markov approach

Published online by Cambridge University Press:  14 July 2016

Mary G. Leitnaker  and
Peter Purdue
Mary G. Leitnaker*
Affiliation:
The University of Tennessee
Peter Purdue
Affiliation:
University of Kentucky
*
∗Postal address: Department of Statistics, The University of Tennessee, Knoxville, TN 37916, USA.
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Abstract

Compartmental models for which transfer from one compartment to another takes a non-negligible time have been studied in the deterministic case. These models rely on the use of differential equations with delayed arguments. In this paper we show how the well-known structure of the semi-Markov process can be used to analyse stochastic compartmental models with transfer delays. Evaluation of the limiting behavior is much simpler in the stochastic model than in previous deterministic formulations. In addition, time-dependent behavior can be analysed using numerical quadrature methods.

Keywords

TIME-LAG PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 570 - 582
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

∗∗

Present address: Probability and Statistics Program, National Science Foundation, Washington, DC 20550, USA.

Research supported by NSF Grant No. MCS8102215–01.

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